Creating superconductivity in WB2 through pressure-induced metastable planar defects

High-pressure electrical resistivity measurements reveal that the mechanical deformation of ultra-hard WB2 during compression induces superconductivity above 50 GPa with a maximum superconducting critical temperature, Tcof 17 K at 91 GPa. Upon further compression up to 187 GPa, the Tcgradually decreases. Theoretical calculations show that electron-phonon mediated superconductivity originates from the formation of metastable stacking faults and twin boundaries that exhibit a local structure resembling MgB2 (hP3, space group 191, prototype AlB2). Synchrotron x-ray diffraction measurements up to 145 GPa show that the ambient pressure hP12 structure (space group 194, prototype WB2) continues to persist to this pressure, consistent with the formation of the planar defects above 50 GPa. The abrupt appearance of superconductivity under pressure does not coincide with a structural transition but instead with the formation and percolation of mechanically-induced stacking faults and twin boundaries. The results identify an alternate route for designing superconducting materials.

The XRD peaks of the WB 2 hP12 and hR6 phases are quite similar, such that the broadening of the experimentally measured XRD peaks at high pressures leads to difficulty in conclusively identifying the stable phase. To check whether a strained lattice of the hR6 phase can account for the experimentally observed high-pressure XRD pattern, we perform the following analysis. We strain the DFT relaxed lattice parameters of the hR6 phase and compare the resulting theoretical XRD pattern against the experimental data. The c lattice parameter was kept unchanged from its DFT value because the experimental XRD peaks that contain contributions from the planes perpendicular to the c-axis match almost perfectly with the theoretical peaks. We performed this analysis at two pressures, 85 GPa and 145 GPa, as shown in Figs.1 and 2. In these figures, the peaks denoted by the star symbol are due to the Re-gasket (cyan) and the Ne pressure-transmitting medium (orange). We observe that the strained hR6 lattice fails to produce the experimentally observed pattern at 85 GPa and 145 GPa. This failure of the strained lattice reveals the absence of significant amounts of the hR6 phase. We further rule out the presence of the hR6 phase with the help of the theoretically calculated critical temperatures. According to our calculations, the hR6 phase has a critical temperature of less than 5 K up to 100 GPa, which is far less than the observed T c of 17 K at 90 GPa.
Supplementary Figure 1: Experimentally measured XRD pattern of WB2 and theoretically calculated peaks of the strained hR6 phase at 85 GPa. The a lattice vector of the structure was strained whereas the c lattice vector was kept unchanged. The legend in each plot indicates the amount by which the a lattice parameter was changed with respect to the DFT relaxed structure.

WB2 STACKING FAULT AND TWIN BOUNDARY
As the pressure applied to the WB 2 samples increases, stacking faults and twin boundary defects can form inside the sample because of mechanical deformation. Here, with the help of Figures 3 and 4, we present how simulation cells containing these planar defects can be created in the WB 2 hP12 phase by sliding W and B planes. Figures 3(a) and 4(a) show the perfect hP12 unit cells. A cell with a stacking fault is created by sliding the appropriate W and B planes along the [1/3, 2/3, 0] vector in the hP12 cell, as shown in Figure 3(b). In Figure 4(b), the simulation cell of the twin boundary is formed by sliding only two successive W and B planes along the [1/3, 2/3, 0] vector. For calculating the defect formation energy depicted in Figure 4(i), we use simulation cells equivalent to four hP12 unit cells. We expect that the buckled Boron layers in the hP3 region will unbuckle and shift by 1/3 of the 'a' lattice vector to lower the energy of the defect structure.

ELECTRONIC STRUCTURE OF WB2 UNDER PRESSURE
The electronic structures of WB 2 in the experimental space group P6 3 /mmc under 0 and 100 GPa are shown in Fig. 5. The states near the Fermi level are mostly tungsten d states and they are important in understanding the superconductivity of WB 2 . Pressure usually has the effect of broadening bandwidth. However, the broadening is not uniform. For example, the band that touches the Fermi level at H point under 0 GPa moves to 0.2 eV below the Fermi level under 100 GPa, while the two bands that merge at A point remain 0.3 eV below the Fermi level. Overall, the density of states evolve smoothly with pressure and the Fermi level falls inside a DOS valley, contrary to the sudden emergence of superconductivity at 50 GPa observed in experiments. In addition, the DFT-estimated electron-phonon coupling of WB 2 in the P6 3 /mmc phase is small and cannot account for the experimental T c , which suggests that the superconductivity might not be due to the P6 3 /mmc phase. On the other hand, the electron-phonon coupling of WB 2 in the MgB 2 structure is strong, pointing to possible existence of local MgB 2 -like structures in certain regions of the experimental sample that is responsible for the superconductivity of WB 2 under pressure.

PRESSURE DEPENDENCE OF PHONON DISPERSION OF WB2 IN THE HP3 PHASE
In recent years, high pressure experiments have played an important role in expanding the frontier of phases of materials that can be stabilized. Structures that are otherwise chemically or dynamically unstable under the ambient condition can be easily pressurized into existence. In this section, we present the pressure dependence of the phonon dispersion of WB 2 , see 6. The phonon spectrum is calculated by running a QE calculation on a coarse mesh first and then an EPW calculation is carried out to interpolated from the coarse k-and q-meshes to much finer meshes. We have assumed harmonic approximation which can already provide important guidance for understanding the experimental data. Anharmonic effects might have some impact on the exact pressure at which the hP 3 phase becomes unstable. However, the issue of anharmonicity is out of the scope of our current manuscript.   Figure 7 shows the decompression behavior of temperature-dependent electrical resistivity of WB 2 in Run 2. The superconducting temperature T c (90%) at 63 GPa (black curve, first compression) is ∼10 K in consistent with Run 1 as shown in Fig. 1d. When lowering the pressure down to 48 GPa (red curve), interestingly T c rather increases to ∼13 K and starts to decrease to ∼3 K at further lowering to 4.9 GPa, which shows the irreversible behavior of T c (P ) under decompression. This shows that the superconducting phase of WB 2 is metastable at low pressure.   Figure 8 shows the second compression behavior of temperature-dependent electrical resistivity of WB 2 after lowering to ambient pressure (opening the DAC) from the first decompression (Fig. S7) in Run 2. The superconductivity begins to appear from 53 GPa (purple curve) with T c ∼ 4 K in consistent with Run 1 as shown in Fig. 1d. The results indicate that the planar defects or twin boundaries responsible for the superconductivity is only (meta)stable under high pressure. HIGH-PRESSURE XRD PATTERNS OF WB 2 UNDER NONHYDROSTATIC PRESSURE CONDITION Figure 9 shows high-pressure XRD measurements under nonhydrostatic pressure condition to 98 GPa. Without using any pressure medium, the pressure chamber is filled with the WB 2 samples in these measurements. The XRD patterns in Fig. 9(a) match with hP12 structure (orange line, calculated at 0 GPa) except for few minor additional peaks appearing above 50 GPa that could be assigned to either hP3 or hR6 phase as possible local defects. However, other large peaks associated with the hP3 and hR6 structures (e.g. peaks near 7-8 degrees) are entirely missing from the experimental data. Figure 9(b) shows the XRD pattern at 98 GPa compared to those of the five competing phases in in Fig. 3 of the main text. The data are not not of sufficient quality to permit a full quantitative Rietveld refinement, but nonetheless, the results confirm that the bulk WB 2 sample still remains predominantly in hP12 phase up to 98 GPa under non-hydrostatic conditions. The results are consistent with the quasi-hydrostatic XRD measurements where Ne was used as the pressure medium (Fig. 2, main text).